cheesemonkey wonders

cheesemonkey wonders

Saturday, August 20, 2016

Week 1 - "very much like being shot out of a cannon" #MTBoSBlaugust

Week 1 is in the can and I wanted to blog one of my best ideas from my first week back.

I should start out by saying that Week 1 was very much like being shot out of a cannon — much more so than usual. My classes this year are huge — 36, 37, or 38 students per class — but my room is the smallest in the school. So it took a lot of clever angling and arranging to ensure that we could have enough desks in the room and that everybody could more or less see from their given position in the room. I always mark on the floor with a Sharpie so that it's easier to put the desk clusters back into their optimal positions. Once upon a time, I would have considered this a form of vandalism, but now...? Hey, that's just common sense.


SEATING CHART MANAGEMENTI had a major conceptual breakthrough with seating charts this August. I always use OmniGraffle to set up my basic seating chart/management chart template that I use on my clipboard to take attendance and make notes. This year, it occurred to me: instead of using those stupid little name card tags with names to make a wall chart (which takes up an unreasonable amount of time), why not just make a board with a sheet of vinyl across to hold blank copies of the week's seating charts?

So now, I  can just print off two copies of my updated charts — one for my clipboard and one for the wall pockets. And voil√°! Easy to change the seats around.

The stapled blob of paper charts makes it super-easy to make notes about collaboration or mathematical successes during group work. It also makes it easy to enter attendance on the computer each class because I just look for the 0s or 1s. My scribbled comments make it easy to enter "Professionalism" scores or comments, or to send e-mails to students or families. My working copy of charts gets stapled together and placed on my clipboard. When the week is over, I archive it in a big binder.

[visualize the dazzling photo of my wall chart that will be posted here on Monday]

There's a lot more to say about Week 1, but I'm still recuperating. More soon!

Hey, Megan, Here's my
handouts hanger in situ!

Friday, August 12, 2016

#MTBoSBlaugust 4 - Dear Pam (starting the year and Exeter Math 1)

Dear Pam,

The closer the start of school gets, the more I realize I need to be wise about how I choose to introduce Exeter problems. I want to set my students up for success. They are an extremely diverse group, coming from all over the city and all over the world. They are new to our huge school and to high school. And my classes are huge. There is still load-balancing to do, but right now my Algebra 1 rosters are topping out at 42. This is a special problem in my room because we can only fit 36 desk-chairs in the room. Literally. So I have to practice basic trust that this is all getting worked out through placement and class balancing and other dark arts of administration.

But all of this thinking has made me realize that I need to rely on my proven, first-two-weeks training plan to get them ready for my course and to help accomplish all of the transitions I am expecting them to manage. Bottom line: I need to start by training them with Talking Points to ensure equity and access for all.

Accordingly, I've created a set of Day 1 Talking Points about ratios, units, and rates (actually for us it's Day 2 because Day 1 is a loss), which are the topics of M1:1#1. I want to use this to train them on norms and practices in my class so that we can begin our problem-based learning together. For me, the first two weeks are critical. They are when I train my students intensively on my rules and norms, using Talking Points and other practices. With 36 students per class, this is a must. Everybody has to get bought in and skilled at the structures so we can proceed.

I also need to work this beginning-of-the-year routine into my four-stage How People Learn groove. Talking Points is my go-to beginning-of-the-year Stage 1 task structure (initial encounter with new concepts and activation of old). Our debrief and shift into doing notes/INB organization is Stage 2 (initial provision of a new expert model).  We'll do some notes on ratios, units, and rates to review and organize our thinking, and then we'll do a little combo-plate Stage 3 / Stage 4 work (deliberate practice with metacognitive / transfer task) in the form of some opening Exeter problems.

I've changed my mind about ordering page 1. I'm going to have them do 1#1 first (easy application of ratios, units, and rates) as a "deliberate practice with metacognitive awareness" problem and then 1#5, the journey of a thousand miles problem (J-1000). What I like about this one as a first transfer task is that it pushes them to use their bodies and to involve their whole selves in the investigation. Once somebody in the class asks, "Hey, Dr. S — can we have a yardstick?" I know I've got them. ;)

From here we can move on to 1#2, which is really the heart of the intro to problem-based learning in my opinion.

But realistically, we won't get to this until Day 3 (which is my true Day 2). So I'm having to accept that this is the reality of where I can get them and when. I can tweak the rest of everything to make it fit the first two weeks, but this is my reality.

So Day 3 needs a new set of Talking Points to begin and then a handout for problem 1#2, the problem about counting non-stop by ones to one billion.

Friday, August 5, 2016

#MTBoSBlaugust 3 - The Bumper Car Theory of Anti-Racist Training for Teachers and Staff

This one is challenging to write because I want to honor all appropriate boundaries while inquiring into my own personal experience of the process.

This next week, during our whole-school PD on Wednesday, we are embarking on our first year of a multi-year program of anti-racist training for teachers and staff. Earlier this summer, I was one of 25 teachers and staff from our school who attended the initial training, and naturally, nothing went as planned. Does it ever? Heavy Sigh. So this morning, we did our reset and met about our plan to do this training with our whole school.

The enterprise of confronting privilege to teach and learn about privilege is daunting, and it is unavoidable that many people who encounter this work will quickly get rubbed raw. In some ways, that is by design. You can't remain comfortable while digging into uncomfortable territory. But at the same time, conceiving the work merely as a project of "disruption" dishonors the good will and long-term focus of individuals who have come together on their own out of their own deep-rooted belief that we need to do better, both for our students and for ourselves.

So you can see how it's a complicated and messy process to get started.

Your face here
What I am coming to understand about it all is this: in order to have courageous conversations about race, we need to learn how to see our own personal invisible beliefs. These are hard to see because they are by nature invisible. They are blind spots. For example, as a high-status, highly educated white teacher, I tend to feel confident in sharing my views publicly; but at the same time, I struggle to keep my passion and confidence from appearing as arrogance to those with different patterns of privilege. And I'm just one individual teacher in a very large faculty. I'm sure that other teachers struggle to notice their own patterns of privilege. Plus the nature of the dominant culture in our school is unusual and complex. So all in all, learning to see the individual and collective belief systems and blind spots is going to be a real challenge. We are going to need to spend a lot of time in a space of collective and individual not-knowing, together. And I fully expect that process to be uncomfortable.

What strikes me most is that this whole process is like being in racial identity bumper cars. Like at a carnival. We need to expect to be disturbed and surprised and confused as we discover how other drivers in their own identity bumper cars interpret and experience life from their own points of view, because everybody is so certain that their own personal bumper car point of view is clear-seeing and constructive and intentional. But every time the ride starts up, whenever you try to steer your own bumper car, you cannot help but crash into other people's bumper cars. So the process of investigation is complicated because there is no way to step outside of the bumper car bumping arena while the inquiry is ongoing.

From the 30,000-foot perspective, I can see that the bumper car system is designed to thwart objectivity. In their own bumper car ride, nobody is 100% in control of their own bumper car. We all have our own projections and privilege and beliefs that we project onto every other driver who crashes into us. If you consider how the bumper cars are designed, you may understand logically that the bumping is unavoidable. But after you've been in the arena for a little while, trying to steer your own car for a bit, it becomes hard not to take things personally. It becomes impossible to avoid lapsing into the belief that other drivers are intentionally crashing into you to push you off course.

I think this model is especially true when you've got a large room full of public school educators — smart, highly educated, open-hearted people who do what they do out of dedication to learning and to contributing to the common good. The moment you start to prod individual teachers into seeing how they benefit from various networks of privilege, things get painful. People shut down or break down. And I've never yet seen it handled well. In our culture, teaching is already pre-constructed as a "Wretched of the Earth"-level of profession. Poorly paid, micro-managed, and bullied by corporate reformers and unelected politicians. What could possibly go wrong when you try to confront public school teachers about privilege?

So I think it is going to take a certain gentleness, determination, and persistence to help a whole faculty to see how we as individuals benefit from different forms and degrees of privilege, both in our school culture and in our society. It is also going to take chocolate and a whole lot of radically appropriate self-care. I am hopeful in the long term that we will make progress, but I suspect that in the near term, things could get messy. Still, I remain optimistic and curious to see how things unfold.

Wednesday, August 3, 2016

#MTBoSBlaugust Post #2: Using Exeter Math 1 — down to brass tacks

I am shamelessly using the #MTBoSBlaugust challenge as a prod to organize my thinking about how to use Exeter Math 1 this year in Algebra 1.

Last year's Algebra 1 implementation was a mess. Not even a hot mess, just a mess. The materials from our district were inadequate and even with my enrichments, I found that the whole was not coherent enough or challenging enough for my students. It also started waaaaaaayyyy too slow out of the gate. And it didn't provide nearly as much work on modeling and sense-making as I wanted.

Other than that, it was fine.

So this year, to start with, here's my game plan for reordering units for the fall semester.

Sequence of Units
  1. Mathematical Modeling and Problem-Solving (EQ: How can we use mathematics and logic to make sense of real-world situations?) 
  2. Equations, Proportions, and Number Lines (EQ: How can we use our existing algebra toolkit to solve equations involving proportions, variables, and absolute value?) 
  3. Lines and Linear Functions (EQ: How do lines and linear functions enable us to analyze and predict real-world phenomena?) 
  4. Functions and Functional Thinking (EQ: How can functions and functional thinking help us in our modeling work?) 
  5. Systems of Linear Equations (EQ: How can we use multiple equations to model real-world situations?) 
  6. Working With Exponents (EQ: What makes exponents such powerful tools?) 
Unit 1 is going to be my two-week mathematical modeling and problem-solving boot camp.

Begin At The Beginning: Unit 1
This is going to work because M1:1 – 8 cover all of the things I want to deal with as review topics anyway, but in a novel and challenging way: rates and units; "micro-" modeling (going from words to mathematics) and functional thinking; using the number line; modeling with non-standard rates, fractions, ratios, and proportions; distributive property and order of operations; "like" terms; and modeling with area and volume.

Meanwhile, the most important thing about the first two weeks is to really drive home my routines and norms and structures. That creates space to get to know students and do some formative assessment so I can make intentional groupings and establish the tone for the course.

This year, the material for the first 9 days will be the first eight pages of lightly adapted Exeter problems, i.e., replacing "Exeter" with my school's name and replacing all the kid names with character names of my own choosing (I tend to favor Batman and the character names from Sesame Street and Harry Potter).

Day 1 is a complete loss because (a) it's a ridiculously short period and (b) we are required to go over our syllabus (don't ask). But I think I will put M1:1#5, which I refer to as J-1000 (the "journey of a thousand miles" problem) on the opening slide as the intro task for students to do once they've found their seats. It's a little bit of math, but it sets the tone I want, which is that we get down to mathematical business in my classroom.

Day 2 is my true Day 1, so that will be my M1:1 day.

Background: Organizing Principles
For any day that I am using a page of Exeter problems, I want to organize the problems according to Bowen and Darryl's PCMI-based framework of Important Stuff / Interesting Stuff / Tough Stuff.

That way, I can also use their twin strategies of (a) intentional groupings (keep the speed demons away from the katamari) and (b) deliberately featuring katamari solutions and insights during whole-class discussion segments. For background on all of this, including PCMI, Bowen, and Darryl's group work strategies, first read Ben Blum-Smith's Lessons from Bowen and Darryl and then my post on Lessons from Lessons from Bowen and Darryl.

Any remaining problems left over from the day's classwork can be done as homework problems that night, and those can then be discussed during the next day's Home Enjoyment/Burning Questions segment. A beautiful thing.

Day 1: M1:1#2
Problem 1:#2 is a perfect rich task for starting off an Algebra 1 course. You can demand that students let go of their habits of learned helplessness and use whatever they know. You can encourage them with problem-solving process hints and without robbing them of the opportunity to do the thinking for themselves.

Everything else on page 1 is just review and activation of prior knowledge.

OK, that's all I've got for page 1.

Monday, August 1, 2016

Scan in your best worked examples #MTBoSBlaugust

This is going to be a short post because I am trying to take my own best advice:

Scan in your best worked examples.
Let me repeat that: Scan in your best worked examples. Scan in your best worked examples.

And if you are just joining us... today's advice is: scan in your best worked examples.

I spent about 2 months working through every problem on every page of Exeter Math 1. All 91 pages of problem sets. And finally, today is ScanFest 2016.

I first learned this advice from Sam Shah (of course), and it bears repeating. Your frazzled, middle-of-the-year self will thank you for it.

And now, back to scanning.

Thursday, June 23, 2016

Exeter Math 1 Reflection 3: A Course in Advanced Proportional Reasoning

This is the third in a who-knows-how-many-part-series I am doing on my experience and practice of doing and using Exeter Math 1 in my Algebra 1 classes. The three labels I am using for this series of posts are: Exeter Math 1, Algebra 1, and metacognition.

As I see it, there are two core developmental strands in Exeter Math 1 that are woven together throughout the course. One strand concerns advanced proportional reasoning. The other involves what I would characterize as Exeter's method of "micro-modeling"—an ongoing spiral of frequent, small, subtle modeling tasks that provide extensive both variety and depth of practice in modeling. Many variations are explored so that students get a lot of practice in making sense of similar and differing contexts.

What I love about this blend of proportional reasoning and micro-modeling is that it occurs at the intersection of advanced textual interpretation and advanced proportional reasoning. This means it is an immersive experience in relentless sense-making and meaning-making as students explore modeling. In this course, mathematical modeling is a full-contact sport. Having worked all the way through the entire course, I can see how it is going to develop great fluency and confidence in modeling for Algebra 1 students, regardless of where they are starting (assuming, of course, that they have the basic prerequisites for Algebra 1 success).

The opening problem sets are deceptively simple, although page 1 problem 2 (from here on out, I'm going to use the Exeter-style notation of 1#2 to mean "page 1 problem #2), would be a fantastic Day 1 in-class rich task that drops students right into a hard micro-modeling problem with whatever tools they have.

But other than 1#2, most of the problems in the first 7 pages are deceptively simple. They're clearly written to review prior knowledge and to establish individual and group norms of work, with the major themes being work on rates, distributive property, order of operations, functional thinking, notation, number line, negatives and opposites, #unitchat, fractions, reciprocals, and rational numbers. Major concept development focuses on distance = rate - time, distributive property, working with various kinds of graphs and graphical representations, and micro-modeling.

And then you arrive at 8#1, and BLAMMO.

This is what I'm thinking of when I talk about a truly rich task blast-off.

I'm not going to give away the punch line here, but this "box within a box" problem is an excellent example of what I mean when I say the course focuses on advanced proportional reasoning. The problem requires a very advanced analysis of many distinct moving parts, along with an ability to track back and explain your thinking. By my count, this problem requires the learner to navigate and articulate issues of area, volume, footprint, a difference of footprints, layering, and negative space. Perhaps you can see other ideas here as well.

So if you're just getting started with Math 1 and wondering what the heck all the fuss is about, I encourage you to hang in there. 

I imagine that we will get to page 8 around the middle to end of the second week of school. And when we do, students should know that the fun is just beginning.  :)

Wednesday, June 22, 2016

Exeter Math 1 Reflection 2: Growing Up as a Mathematical Thinker

This is the second in a who-knows-how-many-part-series I am doing on my experience and practice of doing and using Exeter Math 1 in my Algebra 1 classes. The three labels I am using for this series of posts are: Exeter Math 1, Algebra 1, and metacognition.

First and foremost, Exeter Math 1 is a course in growing up as a mathematical thinker. It is about leveling the playing field between and among rising 9th grade students. 

Here's how I would would frame this journey for students: This is a course in developing your own mathematical self-reliance and resourcefulness as a learner. Your Essential Question is always: How can I exhaust everything I already know before I ask the teacher for help?

You already know an enormous amount of mathematics. In this class, you will need to step forward with that and be willing to attack problems with the best thinking you already have. You may not know everything, but you always know something, and since that something is the best thing you know, you show up and start there and give it everything you've got.

Then, when you have struggled as much as you can and as hard as you can—both by yourself and with your table group—and when you can no longer do anything more with what you've got, that is the appropriate point at which you can ask the teacher for help.

That is the best use of the teacher.

If you are passive in this work or mess around, you are going to suffer.

This course works at two levels. At the content level, we are going to do all of the usual content work in an Algebra 1 class. But the more important work we will do always takes place at a metacognitive level. It is designed to help you learn how you learn advanced mathematics.
____________________________________________________

OK, back to the teacher perspective.

I have a Post-It on the inside-front cover of my binder on which I wrote this:
Exeter discovery is about guided sequential flailing.
 I think this is true. The Exeter Math 1 path definitely involves guided, well-sequenced flailing. It also integrates continual spiraling designed to activate prior knowledge. The purpose is always to discover how much math you already know and can put into service with the problems that are directly in front of you.

There is mathematical content and metacognitive content on each page.

This leads to the issue of practice. In Exeter Math 1, there is a very specific theory of action in the practice problems that are given and in how they are used. There are none of the usual taking-up-time, too-easy practice problems. If students need extra practice on certain specific procedures, then you have to source them yourself from someplace else, such as (for us) the Holt Algebra 1 textbook.

But that is OK because at this point in my career, I can do that in my sleep.

The Exeter Math 1 approach to practice problems is to provide juicy, meaningful, gimmick-free practice problems that are (a) always of medium difficulty or above and (b) integrated with metacognitive reflection and discussion. For this reason, I would be inclined to use these inflection points in the curriculum as opportunities to use Talking Points to solidify conceptual understanding and to get students exploring and articulating the subtle misconceptions and potential pitfalls inherent in practice problems of a medium level of difficulty or above.

This is a very deep teaching idea to me — to keep practice problems at or above a medium level of difficulty and to have students explore and give voice to these subtleties as rich opportunities to make meaning in their work.

More thoughts coming soon.